how to change snapping degree
The Snap uses the object's Z axis to stick perpendicularly to the target face, so in your case you need to rotate the origin 90°, at least temporarily:

Enable the Affect Only Origins option in the Options panel on the top right of your 3D view:



Rotate the origin so that its Z axis points perpendicularly to its current orientation:



Disable the option, move your object until it snaps to the face you want:


You could also simply stick the object and rotate it on its own X or Y axis with R and double X or double Y.